GNSS World of China

Volume 47 Issue 2
May  2022
Turn off MathJax
Article Contents
Article Navigation >  GNSS World of China  > 2022  >  47(2): 82-89
WENG Ye, SHAO Desheng, GAN Shu. Ridge estimation method for linearized general EIV adjustment model[J]. GNSS World of China, 2022, 47(2): 82-89. doi: 10.12265/j.gnss.2021083001
Citation: WENG Ye, SHAO Desheng, GAN Shu. Ridge estimation method for linearized general EIV adjustment model[J]. GNSS World of China, 2022, 47(2): 82-89. doi: 10.12265/j.gnss.2021083001
shu

Ridge estimation method for linearized general EIV adjustment model

doi: 10.12265/j.gnss.2021083001
  • 1.

    Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China

  • 2.

    Yunnan Earthquake Agency, Kunming 650041, China

  • 3.

    Plateau Mountain Spatial Information Survey Technique Application Engineering Research Center at Yunnan Province’s University, Kunming 650093, China

  • Received Date: 2021-08-30
  • Accepted Date: 2022-03-01
    • Available Online: 2022-04-14
    Abstract
  • As a general form of classical adjustment model, general errors-in-variables (EIV) adjustment model has the advantage of taking into account multiple random errors. Based on the linear estimation of the weighted total least squares of the general EIV adjustment model, the regularization criterion is introduced. When the regularization matrix is the unit matrix, it is called the ridge estimation. The objective function is then added. By establishing the minimization solution of the Lagrange objective function, the ridge estimation solution corresponding to the weighted general EIV adjustment model is derived. The U curve method and L curve method for determining ridge parameters are given. The linear estimation, two ridge estimations and their corresponding variance components of the general EIV adjustment model are calculated. It is validated that ridge estimation can promote the linearization estimation of general EIV model, reduce the times of iterations, make the parameter variance component more stable and reduce the calculation of parameter estimation.

     

    • FullText(HTML)
  • loading
    • References(21)
  • [1]
    VAN HUFFEL S, VANDEWALLE J. The total least squares problem: computational aspects and analysis [M]. Philadelphia: Society for Industrial and Applied Mathematics, 1991.
    [2]
    ADCOCK R J. A note on the method of least squares[J]. The analyst, 1877, 4(6): 183-184. DOI: 10.2307/2635777
    [3]
    GOULUB G H, LOAN V C F. An analysis of the total least squares problem[J]. SIAM journal on numerical analysis, 1980, 17(6): 883-893. DOI: 10.1137/0717073
    [4]
    张俏, 徐爱功, 祝会忠, 等. BDS总体最小二乘整周模糊度解算方法[J]. 导航定位学报, 2017, 5(1): 65-69,80.
    [5]
    武曙光, 聂桂根, 彭凤友, 等. 高精度GPS超短基线场数据处理与分析[J]. 全球定位系统, 2020, 45(2): 7-12.
    [6]
    何安良, 张品超, 程兴保. 稳健加权整体最小二乘法在GPS高程拟合中的应用[J]. 江西科学, 2019, 37(4): 549-552,574.
    [7]
    潘雪琛, 姜挺, 余岸竹, 等. 总体最小二乘平差下的基准影像辅助国产卫星影像定位[J]. 测绘通报, 2019(3): 57-60.
    [8]
    曾文宪, 方兴, 刘经南, 等. 通用EIV平差模型及其加权整体最小二乘估计[J]. 测绘学报, 2016, 45(8): 890-894. DOI: 10.11947/j.AGCS.2016.20150156
    [9]
    AMIRI-SIMKOORI A R, MORTAZAVI, ASGARI J. Weighted total least squares applied to mixed observation model[J]. Survey review, 2016, 48(349): 278-286. DOI: 10.1179/1752270615Y.0000000031
    [10]
    曾文宪, 刘泽邦, 方兴, 等. 通用EIV平差模型的线性化估计算法[J/OL]. (2021-01-12)[2021-07-30]. 武汉大学学报(信息科学版). https://doi.org/10.13203/j.whugis20200243
    [11]
    吴光明, 鲁铁定. 病态数据处理的岭估计迭代解法[J]. 大地测量与地球动力学, 2019, 39(2): 178-183.
    [12]
    王乐洋, 许才军, 鲁铁定. 病态加权总体最小二乘平差的岭估计解法[J]. 武汉大学学报(信息科学版), 2010, 35(11): 1346-1350.
    [13]
    陈帅, 詹本勇. 基于L曲线法的抗差岭估计模型[J]. 全球定位系统, 2014, 39(5): 41-45.
    [14]
    林东方, 朱建军, 宋迎春, 等. 正则化的奇异值分解参数构造法[J]. 测绘学报, 2016, 45(8): 883-889. DOI: 10.11947/j.AGCS.2016.20150134
    [15]
    HANSEN P C. Analysis of discrete Ill-posed problems by means of the L-Curve[J]. SIAM review, 1992, 34(4): 561-580. DOI: 10.1137/1034115
    [16]
    鲁洋为, 王振杰. 用U曲线法确定岭估计中的岭参数[J]. 导航定位学报, 2015, 3(3): 132-134,138.
    [17]
    KRAWCZKY-STANDO D, RUDNICKI M. Regularization parameter selection in discrete Ill-posed problems — the use of the U-Curve[J]. International journal of applied mathematics and computer science, 2007, 17(2): 157-164. DOI: 10.2478/v10006-007-0014-3
    [18]
    GOLUB G H, HEATH M, WAHBA G. Generalized cross-validation as a method for choosing a good ridge parameter[J]. Technometrics, 1979, 21(2): 215-223. DOI: 10.1080/00401706.1979.10489751
    [19]
    戴吾蛟, 冯光财, 朱建军. 一种基于Helmert方差分量估计的岭参数确定方法[J]. 大地测量与地球动力学, 2006, 4(4): 30-33.
    [20]
    FIERRO R D, GOLUB G H, HANSEN P C, et al. Rcgularization by truncated total least squares[J]. SIAM journal on scientific and statistical computing, 1997, 18(4): 1223-1241. DOI: 10.1137/S1064827594263837
    [21]
    WANG L Y, XU G Y. Variance component estimation for partial errors-in-variables models[J]. Studia geophysica et geodaetica, 2016, 60(1): 35-55. DOI: 10.1007/s11200-014-0975-2
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(2)  / Tables(4)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (185) PDF downloads(7) Cited by()
    Proportional views
    Related

    Copyright © 2009《 GNSS World of China 》 Editorial Office

    Address：84 Jianshe Dong Lu, Muye District, Xinxiang City, Henan Province, ChinaChina Pos：453000Tel：0373-3712411Fax：0373-3052232Email：qqdwxt@126.com

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return